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When we convert numbers from scientific notation to decimal form, we essentially remove the power of 10 by shifting the decimal point. The direction and number of shifts depend on the exponent.
For example, in the exercise, they converted two numbers given in scientific notation to decimal form.
Let's unpack the steps:
The scientific notation is in the form: \(a \times 10^n\) where \(a\) is the coefficient (a number between 1 and 10) and \(n\) is the exponent (indicating how many places to move the decimal point).

For the number \(1.6 \times 10^{10}\) (part a):

• The exponent is 10 (positive), so you move the decimal point 10 places to the right.
• \(1.6\) becomes \(16000000000\) (16 followed by 9 zeros, as the decimal moves right).

For the number \(8.43 \times 10^{-6}\) (part b):

• The exponent is -6 (negative), so you move the decimal point 6 places to the left.
• \(8.43\) becomes \(0.00000843\) (with 5 zeros in front of 843).

Understanding these steps ensures that you can confidently convert any number from scientific notation to its decimal form.

Positive exponents in scientific notation indicate the number of times the decimal point should be moved to the right.
Here are some key points to remember:

• A positive exponent means the number gets larger.
• For example, \(7.1 \times 10^3\) means you move the decimal point 3 places to the right: \(7100\).
• It simplifies the writing of very large numbers, making them easier to read and use in calculations.

When we see a positive exponent, we should always shift the decimal point to the right and add zeros if necessary to maintain the number’s magnitude.
In the initial example, for \(1.6 \times 10^{10}\), shifting the decimal 10 places to the right turns \(1.6\) into \(16000000000\), yielding a much larger number.

Negative exponents in scientific notation denote the number of times the decimal point should be moved to the left.
Key points to consider:

• A negative exponent means the number gets smaller.
• For instance, \(3.2 \times 10^{-4}\) means shifting the decimal point 4 places to the left, resulting in \(0.00032\).
• This makes dealing with very small numbers more manageable and easier to comprehend.

Whenever we encounter a negative exponent, we should move the decimal point to the left, adding zeros as necessary to reflect the small size of the number.
In the original example, \(8.43 \times 10^{-6}\) with an exponent of -6 meant moving the decimal 6 places left, resulting in \(0.00000843\), a very small number.